IDEAS home Printed from https://ideas.repec.org/a/vrs/stintr/v20y2019i4p153-166n2.html
   My bibliography  Save this article

On Permutation Location–Scale Tests

Author

Listed:
  • Polko-Zając Dominika

    (Department of Statistics, Econometrics and Mathematics, University of Economics in Katowice, Katowice, Poland .)

Abstract

Statisticians are constantly looking for methods of statistical inference that would be both effective and would require meeting as few assumptions as possible. Permutation tests seem to fit here, as using them makes it possible to perform statistical inference in situations where classical parametric tests do not work. Permutation tests appear to be comparably powerful to parametric tests, but require meeting fewer assumptions, e.g. regarding the size of the sample or the from of distribution of the tested variable in a population. The presented tests make it possible to verify the overall hypothesis about the identity of both location and scale parameters in the studied populations. In literature, the Lepage test and the Cucconi test are most often referred to in this context. The paper considers various forms of test statistics, and presents a simulation study carried out to determine the size and power of the tests under normality. As the study demonstrated, the advantage of the proposed method is that it can be applied to small-size samples. A nonparametric, complex procedure was used to assess the overall ASL (achieved significance level) value by applying the permutation principle. For comparative purposes, the results for the permutation Lepage test and the permutation Cucconi test are also presented.

Suggested Citation

  • Polko-Zając Dominika, 2019. "On Permutation Location–Scale Tests," Statistics in Transition New Series, Statistics Poland, vol. 20(4), pages 153-166, December.
    • Handle: RePEc:vrs:stintr:v:20:y:2019:i:4:p:153-166:n:2
    DOI: 10.21307/stattrans-2019-039
    as

    Download full text from publisher

    File URL: https://doi.org/10.21307/stattrans-2019-039
    Download Restriction: no
    File URL: https://libkey.io/10.21307/stattrans-2019-039?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Lunde A. & Timmermann A., 2004. "Duration Dependence in Stock Prices: An Analysis of Bull and Bear Markets," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 253-273, July.
    2. Murakami, Hidetoshi, 2007. "Lepage type statistic based on the modified Baumgartner statistic," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 5061-5067, June.
    3. Lim, Tjen-Sien & Loh, Wei-Yin, 1996. "A comparison of tests of equality of variances," Computational Statistics & Data Analysis, Elsevier, vol. 22(3), pages 287-301, July.
    4. Luigi Salmaso & Aldo Solari, 2005. "Multiple aspect testing for case-control designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 62(2), pages 331-340, November.
    5. Marco Marozzi, 2009. "Some notes on the location–scale Cucconi test," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 629-647.
    6. Marco Marozzi, 2012. "A combined test for differences in scale based on the interquantile range," Statistical Papers, Springer, vol. 53(1), pages 61-72, February.
    7. Marozzi, Marco, 2004. "A bi-aspect nonparametric test for the two-sample location problem," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 639-648, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Dominika Polko-Zając, 2019. "On Permutation Location–Scale Tests," Statistics in Transition New Series, Polish Statistical Association, vol. 20(4), pages 153-166, December.
    2. Marco Marozzi, 2014. "The multisample Cucconi test," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 23(2), pages 209-227, June.
    3. Amitava Mukherjee & Marco Marozzi, 2019. "A class of percentile modified Lepage-type tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(6), pages 657-689, August.
    4. Harding, Don & Pagan, Adrian, 2011. "An Econometric Analysis of Some Models for Constructed Binary Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 86-95.
    5. Song, Zhi & Mukherjee, Amitava & Zhang, Jiujun, 2021. "Some robust approaches based on copula for monitoring bivariate processes and component-wise assessment," European Journal of Operational Research, Elsevier, vol. 289(1), pages 177-196.
    6. Alain-Philippe Fortin & Patrick Gagliardini & O. Scaillet, 2022. "Eigenvalue tests for the number of latent factors in short panels," Swiss Finance Institute Research Paper Series 22-81, Swiss Finance Institute.
    7. Jia Liu & John M. Maheu & Yong Song, 2024. "Identification and forecasting of bull and bear markets using multivariate returns," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(5), pages 723-745, August.
    8. Dumitriu, Ramona & Stefanescu, Razvan & Nistor, Costel, 2010. "Systematic risks for the financial and for the non-financial Romanian companies," MPRA Paper 41636, University Library of Munich, Germany, revised 28 Feb 2010.
    9. Li, Ziran & Sun, Jiajing & Wang, Shouyang, 2013. "Amplitude-Duration-Persistence Trade-off Relationship for Long Term Bear Stock Markets," MPRA Paper 54177, University Library of Munich, Germany.
    10. Ryan C. Erps & Kimihiro Noguchi, 2020. "A Robust Test for Checking the Homogeneity of Variability Measures and Its Application to the Analysis of Implicit Attitudes," Journal of Educational and Behavioral Statistics, , vol. 45(4), pages 403-425, August.
    11. B M, Lithin & chakraborty, Suman & iyer, Vishwanathan & M N, Nikhil & ledwani, Sanket, 2022. "Modeling asymmetric sovereign bond yield volatility with univariate GARCH models: Evidence from India," MPRA Paper 117067, University Library of Munich, Germany, revised 05 Jan 2023.
    12. Sabri Boubaker & Zhenya Liu & Yaosong Zhan, 2022. "Risk management for crude oil futures: an optimal stopping-timing approach," Annals of Operations Research, Springer, vol. 313(1), pages 9-27, June.
    13. Yongli Sang, 2021. "A Jackknife Empirical Likelihood Approach for Testing the Homogeneity of K Variances," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(7), pages 1025-1048, October.
    14. Pesaran, M. Hashem & Timmermann, Allan, 2009. "Testing Dependence Among Serially Correlated Multicategory Variables," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 325-337.
    15. Chiang, Min-Hsien & Huang, Hsin-Yi, 2011. "Stock market momentum, business conditions, and GARCH option pricing models," Journal of Empirical Finance, Elsevier, vol. 18(3), pages 488-505, June.
    16. Yuanyuan Zhang & Stephen Chan & Jeffrey Chu & Hana Sulieman, 2020. "On the Market Efficiency and Liquidity of High-Frequency Cryptocurrencies in a Bull and Bear Market," JRFM, MDPI, vol. 13(1), pages 1-14, January.
    17. Min-Hsien Chiang & Tsai-Yin Lin & Chih-Hsien Jerry Yu, 2009. "Liquidity Provision of Limit Order Trading in the Futures Market Under Bull and Bear Markets," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 36(7-8), pages 1007-1038.
    18. Tommaso Proietti, 2024. "Ups and (Draw)Downs," CEIS Research Paper 576, Tor Vergata University, CEIS, revised 03 May 2024.
    19. Eric Girardin & Zhenya Liu, 2003. "The Chinese Stock Market: A Casino with 'Buffer Zones'?," Journal of Chinese Economic and Business Studies, Taylor & Francis Journals, vol. 1(1), pages 57-70.
    20. Mahadeo, Scott M.R. & Heinlein, Reinhold & Legrenzi, Gabriella D., 2019. "Energy contagion analysis: A new perspective with application to a small petroleum economy," Energy Economics, Elsevier, vol. 80(C), pages 890-903.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:vrs:stintr:v:20:y:2019:i:4:p:153-166:n:2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Peter Golla (email available below). General contact details of provider: https://stat.gov.pl/en/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.